Decoupled, second-order accurate in time and unconditionally energy stable scheme for a hydrodynamically coupled ternary Cahn-Hilliard phase-field model of triblock copolymer melts

In this paper, we first formulate a hydrodynamically coupled phase-field model for triblock copolymer melts and then develop a time-marching scheme for it. The numerical scheme is based on a combination of the projection method and the IEQ (Invariant Energy Quadratization) method to achieve linear and second-order accuracy in time. To further simplify its implementation, we introduce a new nonlocal variable and its time evolution equation, so we end up with a fully decoupled scheme. Under the premise of satisfying strict unconditional energy stability, the scheme only needs to solve several completely independent elliptic equations with constant coefficients at each time step. We provide the rigorous energy stability proof, the detailed implementation of the proposed scheme, and further perform some numerical simulations of triblock polymer materials under applied shear flow in 2D and 3D to demonstrate the effectiveness of the developed numerical scheme.